MME 2001 MATERIALS SCIENCE 1 13.10.2015

outline ● overview of last lecture

periodic table / electronegativity

Classification of elements / interatomic

bonding

● Structure of solids:

crystaline vs noncrystalline

Crystal systems;

BCC, FCC, HCP

atomic packing

crystallographic directions, planes

● QUIZ (will start at 14:50 p.m. !)

The Periodic Law

Mendeleev realized that:

When arranged by increasing atomic

number, the chemical elements display a

regular and repeating pattern of chemical

and physical properties.

what are these properties?

Metallic vs nonmetallic character

Atomic radius

Ionization energies (energy necessary to remove

the outermost electron from the atom)

Electron affinities (energy change when an

electron is added to a neutral atom)

Reactivity

Electronegativity

Organisation of the periodic table

The vertical columns: groups from 1 to 18.

Elements in the same group have similar valence

electron structures

and hence similar

chemical and

physical

properties.

groups

elements are situated, with increasing atomic

number, in seven horizontal rows

called periods.

Each contains

elements with

electrons in the

Same outer shell.

Organisation of the periodic table

periods

Periodic table

Periodic Table metallic character

nonmetallic character meta

llic

chara

cte

r

nonm

eta

llic

chara

cte

r

İoniz

ati

on e

nerg

y

Negati

ve e

lectr

on a

ffin

ity

İonization energy

Negative electron affinity

Atomic radii

Ato

mic

radii

Ionization Energy

IE = energy required to remove an

electron from an atom in the gas phase.

Mg (g) + 738 kJ ---> Mg+ (g) + e-

● the tendency of an atom to attract electrons

towards itself.

● Atoms are more likely to accept electrons if their

outer shells are almost full, and if they are less

“shielded” from (i.e., closer to) the nucleus.

Electronegativity

electronegativity

increases!

Electronegativity

Electronegativity

Metals, Nonmetals & Metalloids 1

2

3

4

5

6

7

Metals

Metalloids

Nonmetals

Metals 88 elements are metals or metal like element

Physical properties:

good conductors of heat and electricity

shiny

ductile (can be stretched into thin wires)

malleable (can be pounded into thin sheets)

High density (heavy for their size)

High melting point

chemical properties:

Easily lose electrons

Form positive (+) ions

Corrode easily

Non-metals Their characteristics are opposite to those of metals.

Physical Properties of Nonmetals:

No luster (dull appearance)

Poor conductor of heat and electricity

Brittle (breaks easily)

Not ductile

Not malleable

Low density

Low melting point

Many non-metals are gases.

Non-metals Chemical Properties of Non-metals:

Tend to gain electrons

metals that tend to lose electrons but nonmetals

that tend to gain electrons, to form compounds

with each other.

These compounds are called

ionic compounds.

When two or more

nonmetals bond with

each other, they form

a covalent compound.

Metalloids Metalloids (metal-like) have properties of both

metals and non-metals.

They are solids

can be shiny or dull

They conduct heat

and electricity better

than non-metals but

not as well as metals

They are ductile and

malleable

interatomic bonding

● the bonding involves the valence electrons

● the nature of the bond depends on the electron

structures of the constituent atoms.

● There are three types of bonding: each bonding

type arises from the tendency of the atoms to

assume stable electron structures.

● Secondary or physical forces and energies are

weaker than the primary ones, but nonetheless

influence the physical properties of some

materials.

interatomic bonding Ionic

Metal (cation) with non-metal (anion)

Transfer of electron(s)

Strong bond high melting point

Covalent

Non-metal with non-metal

Sharing of electron(s)

Non-polar (equal distribution of electrons)

Polar (uneven electron distribution)

Weak bonds…low melting points

Metallic (nuclei in a “sea” of shared electrons)

● Forms between metallic and nonmetallic

elements; elements at the horizontal extremities

of the periodic table.

● a metallic atom easily gives up its valence

electrons to the nonmetallic atoms.

● In the process all the atoms acquire stable

configurations and become ions.

● Ionic bonding is non-directional (magnitude of the

bond is equal in all directions around the ion)

● Ceramic materials exhibit ionic bonding

ionic bonding

• Occurs between + and - ions.

• Requires electron transfer.

• Large difference in electronegativity required.

Ionic Bonding

Na (metal)

Unstable

11 electrons

Cl (nonmetal) Unstable

17 electrons electron

+ -

Coulombic Attraction

Na (cation) stable

Cl (anion) stable

positive and negative ions, by virtue of their net electrical charge, attract one another

• Predominant bonding in Ceramics

Ionic Bonding - examples

Give up electrons Acquire electrons

NaCl

MgO

CaF 2

CsCl

Ion Sizes

CATIONS are SMALLER than the atoms from

which they come.

The electron/proton attraction has gone UP

and so size DECREASES.

Li,152 pm 3e and 3p e

Li + , 78 pm 2e and 3 p

+ Forming

a cation.

Ion Sizes

ANIONS are LARGER than the atoms from

which they come.

The electron/proton attraction has gone DOWN

and so size INCREASES.

Trends in ion sizes are the same as atom sizes.

Forming

an anion. F, 71 pm 9e and 9p + e

F - , 133 pm 10 e and 9 p

-

● The predominant bonding in ceramic materials

is ionic.

● Ionic materials are characteristically hard and

brittle and, electrically and thermally

insulative.

● These properties are directly related to

electron configurations and/or the nature of the

ionic bond.

ionic bonding

covalent bonding ● stable electron configurations are assumed by the

sharing of electrons between adjacent atoms.

● Two atoms that are covalently bonded will each

contribute at least one electron to the bond, and

the shared electrons may be considered to belong

to both atoms.

● The covalent bond is directional; it is between

specific atoms and may exist only in the direction

between one atom and another that participates

in the electron sharing.

C: has 4 valence e-,

needs 4 more

H: has 1 valence e-,

needs 1 more

Electronegativities

are comparable.

Covalent Bonding ● similar electronegativity share electrons

● bonds are determined by valence –

● s & p orbitals dominate bonding

● Example: CH4 shared electrons

of carbon atom

shared electrons of hydrogen atom

H

H

H

H

C

CH 4 H

∙∙

H : C : H

∙∙

H

covalent bonding ● Covalent bonds may be very strong, as in

diamond, which is very hard and has a very high

melting temperature, 3550 C, or they may be

very weak, as with bismuth, which melts at about

270 C.

● Polymeric materials typify this bond, the basic

molecular structure often being a long chain of

carbon atoms that are covalently bonded together

with two of their available four bonds per atom.

● The remaining two bonds normally are shared

with other atoms, which also covalently bond.

covalent bonding ● interatomic bonds may be partially ionic and

partially covalent.

● very few compounds exhibit pure ionic or covalent

bonding.

● the degree of either bond type depends on the

relative positions of the components in the periodic

table or the difference in their electronegativities.

● The wider the separation (the greater the difference

in electronegativity), the more ionic the bond.

● the closer they are (the smaller the difference in

electronegativity), the greater the degree of

covalency.

interatomic bonding

No electronegativity difference between two

atoms leads to a purely non-polar covalent bond.

A B

A small electronegativity difference leads to a

polar covalent bond.

A B

A large electronegativity difference leads to an

ionic bond.

metallic bonding ● Metallic materials have one, two, or at most,

three valence electrons.

● these valence electrons are more or less free to

drift throughout the entire metal and form a “sea

of electrons”.

● the metallic bond is nondirectional in character.

The free electrons act as a “glue” to hold the ion

cores together.

● Bonding may be weak or strong; bonding energy 68

kJ/mol (0.7 eV/atom) for mercury and 849 kJ/mol

(8.8 eV/atom) for tungsten. Their respective

melting temperatures are 39 and 3410 C.

metallic bonding

Secondary-van der waals-bonding Secondary, van der Waals, or physical bonds are

weak in comparison to the primary or chemical

ones; bonding energies are typically on the order

of only 10 kJ/mol (0.1 eV/atom).

Secondary bonding exists between virtually all

atoms or molecules, but its presence may be

obscured if any of the three primary bonding types

is present.

Secondary bonding is evidenced for the inert gases,

which have stable electron structures, and, in

addition, between molecules in molecular

structures that are covalently bonded.

Properties linked with bonding

r o r

Energy

if the bond energy is higher,

● Melting point is higher

● Thermal expansion

coefficient is smaller

● Elastic modulus is

higher

Ceramics

(Ionic & covalent bonding):

Metals

(Metallic bonding):

Polymers

(Covalent & Secondary):

Large bond energy

high Tm

high E

small

Variable bond energy

moderate Tm

moderate E

moderate

Directional Properties

Secondary bonding dominates

small Tm

small E

high

Primary Bonds

structure of solids

Non dense, random packing

Dense, ordered packing

Dense, ordered packed

structures tend to have lower energies!

Energy and Packing Energy

r

typical neighbour

bond length

typical neighbour bond energy

Energy

r

typical neighbour bond length

typical neighbour bond energy

Crystalline materials:

atoms are situated in a

repeating array over large

atomic distances;

long-range order exists..

each atom is bonded to its

nearest-neighbor atoms.

typical of:

metals

many ceramics

some polymers

crystalline SiO2

Materials and Packing

Si Oxygen

noncrystalline solids

noncrystalline SiO2

noncrystalline materials:

no periodic packing of atoms

occurs in the case of

complex structures

rapid solidification

amorphous = noncrystalline

many polymers

some ceramics

? metallic glasses

Si Oxygen

crystalline SiO2

Materials and Packing

Si Oxygen

noncrystalline SiO2

● crystalline vs amorphous solid

depends on the ease with which a random

atomic structure in the liquid can transform to

an ordered state during solidification.

● Therefore, amorphous materials are

characterized by atomic or molecular structures

that are relatively complex and become

ordered only with some difficulty.

noncrystalline solids

● rapid cooling through the freezing temperature

noncrystalline solid / no time for ordering!

● metals normally form crystalline solids

● some ceramic materials are crystalline, whereas

others, the inorganic glasses, are amorphous.

● polymers may be completely noncrystalline and

semicrystalline consisting of varying degrees of

crystallinity.

noncrystalline solids

noncrystalline solids

noncrystalline

crystalline

T

t

metals

dT/dt

noncrystalline solids

noncrystalline

crystalline

T

t

ceramics

dT/dt

● How do atoms assemble into solid

structures? (we shall focus on metals for

the time being!)

● How does the density of a material depend

on its structure?

● When do material properties vary with the

sample (i.e., part) orientation?

Structure of solids issues of interest

Structures of crystalline solids

● properties of crystalline solids depend on the

crystal structure of the material, the manner in

which atoms are spatially arranged.

● For example, magnesium, having one crystal

structure, is much more brittle (i.e., fracture at

lower degrees of deformation) than aluminium

that has yet another crystal structure.

magnesium

aluminium

Structure – mechanical properties

● significant property differences exist between

crystalline and noncrystalline materials having

the same composition.

● For example, noncrystalline ceramics and

polymers normally are optically transparent; the

same materials in crystalline form tend to be

opaque or, at best, translucent.

Alumina

Single crystal

Polycrystal-low porosity

high porosity

structure – physical properties

structure of crystalline solids

● atomic hard-sphere model: atoms (or ions) are

thought of as being solid spheres having well-

defined diameters. These spheres touch one

another.

● the unit cell is the basic structural unit or

building block of the crystal structure and

defines the crystal structure by virtue of its

geometry and the atom positions.

metallic crystal structures ● metallic bonding

● nondirectional: minimal restrictions as to the

number and position of nearest-neighbor atoms

● hence, relatively large numbers of nearest

neighbors

● three relatively simple crystal structures are

found for most of the common metals:

face centered cubic (FCC)

body-centered cubic (BCC)

hexagonal close-packed (HCP)

51

metallic crystal structures tend to be densely packed.

Reasons for dense packing:

● Typically, only one element is present, so all

atomic radii are the same.

● bonding is not directional.

● nearest neighbor distances tend to be small in

order to reduce bond energy (energy minimization).

● electron cloud shields cores from each other

● have the simplest crystal structures.

metallic crystal structures

crystal systems Unit cell: smallest repetitive volume which

contains the complete lattice pattern of a crystal.

The unit cell geometry is completely defined in

terms of six lattice parameters

edge lengths: a, b, and c

(lattice constants)

interaxial angles:

, , and (lattice angles)

There are seven different

possible combinations of

a, b, and c, and , and

crystal systems

7 distinct crystal systems

cubic

tetragonal

hexagonal

orthorhombic

rhombohedral

monoclinic

triclinic

14 crystal lattices

crystal systems cubic: a=b=c, ===90

simple

cubic

body-centered

cubic (BCC)

face-centered

cubic (FCC)

body-centered

tetragonal (BCT)

simple

tetragonal

tetragonal: a=bc, ===90

crystal systems

monoclinic: abc, ==90

simple

monoclinic

base-centered

monoclinic

orthorombic: abc, ===90

simple body-centered base-centered face-centered

crystal systems

Total of 14 Bravais lattices!

triclinic

abc,

90

hexagonal

a=bc,

==90 =120

rhombohedral

a=b=c,

==90

crystal systems

maximum symmetry minimum symmetry

triclinic

abc

90

cubic

a=b=c

===90

metallic crystal structures

How can we stack metal atoms to minimize

empty space?

2-dimensions

vs

cube 6 faces

8 corners

12 edges

hard-sphere unit cell

reduced-sphere unit cell

aggregate of many atoms

metallic crystal structures F.C.C. Crystal structure:

simple cubic structure (SC)

• Coordination # = 6

(# nearest neighbors)

• Rare due to low packing density

(only Po has this structure)

• Close-packed directions are cube edges.

● Atoms touch each other along cube edges.

● each of 8 corner atoms is shared by eight unit

cells:

8 x (1/8) = 1 atom/unit cell

simple cubic (SC) structure

unit cell

volume = a3 = 8R3

R

a = 2R

BCC crystal structure ● unit cell has cubic geometry

● atoms are located at the corners of the cube.

● Some of the materials that have a bcc structure

include lithium, sodium, potassium, chromium,

barium, vanadium, alpha-iron and tungsten.

● Metals which have a BCC structure are usually

harder and less malleable than close-packed

metals such as copper and gold.

● When the metal is deformed, the planes of

atoms must slip over each other, and this is more

difficult in the bcc structure.

Coordination # = 8

Body Centered Cubic Structure (BCC)

Atomic packing of

an BCC (110)

plane.

1 2

4 3

5 6

7 8

● Atoms touch each other along cube diagonals.

● each of 8 corner atoms is shared by eight unit

cells; single center atom is wholly owned:

8 x (1/8) + 1 = 1 + 1 = 2 atoms/unit cell

● each center atom touches eight corner atoms:

8 nearest neighbors

body centred cubic (BCC) structure

3.a = 4R 2.a

a

FCC crystal structure

● unit cell has cubic geometry

● atoms are located at the corners and the

centers of all the cube faces.

● familiar metals with FCC crystal structure

copper

aluminium

silver

gold

Reduced sphere FCC unit cell with the (110) plane.

Atomic packing of an FCC (110) plane.

Atomic arrangements - FCC

Atoms touch each other along face diagonals.

Coordination # = 12

The face-centered atom in the front face is in contact

with four corner atoms and four other face-centered

atoms behind it (two sides, top and bottom) and is

also touching four face-centered atoms of the unit

cell in front of it.

Face Centered Cubic Structure (FCC)

atoms touch one another across

a face diagonal; cube edge length

a and the atomic radius R

a2 + a2 = (R+2R+R)2

2a2 = (4R)2 = 16R2

a2 = 8R2

a = 2R2

R = a /(22)

FCC crystal structure

a R

2R R

each of 8 corner atoms is shared by eight unit cells;

each of 6 face-centered atoms belongs to only two.

8 x (1/8) + 6 x (1/2) = 1 + 3 = 4 atoms/unit cell

The volume of the unit cell,

a3 = (2R2)3 = 16R32

FCC crystal structure

4R=2.a (a = 2R2)

cubic crystal structures

X’tal structure Coordination # Atoms/unit cell

simple cubic 6 1

body centred 8 2

face centred 12 4

atomic packing factor (APF)

APF is the sum of the sphere volumes of all

atoms within a unit cell divided by the unit

cell volume:

the maximum packing possible for spheres

all having the same diameter.

APF =

a 3

4

3 (0.5a) 3 1

atoms

unit cell atom

volume

unit cell

volume

Atomic Packing Factor (APF)-SC

APF = Volume of atoms in unit cell

Volume of unit cell

close-packed directions

a

R=0.5a

contains 8 x 1/8 = 1 atom/unit cell 1

APF for a simple cubic structure = 0.52

Atomic Packing Factor: BCC

a

APF =

4

3 ( 3 a/4 )

3 2

atoms

unit cell atom volume

a 3 unit cell

volume

length = 4R = Close-packed directions:

3 a

APF(BCC)= 0.68

a R

a 2

a 3

2a

4R

a

2 a

Atomic Packing Factor: FCC

APF =

4

3 p ( 2 a/4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell volume

Close-packed directions: length = 4R = 2 a

Unit cell contains:

6 x 1/2 + 8 x 1/8

= 4 atoms/unit cell

= 0.74 maximum

achievable APF

Closed packed crystal structures

A portion of

a close-packed

plane of

atoms; A, B, and

C positions

are indicated.

The AB

stacking

sequence for

close packed

atomic planes.

Hexagonal close packed (HCP) crystal structure Not all metals have unit cells with cubic symmetry;

some common metals have a hexagonal structure

Atomic alignment repeats every other plane!

The real distinction between FCC and HCP

lies in where the third close-packed

layer is positioned. For HCP, the centers

of this layer are aligned directly above

the original A positions.

stacking sequence, ABABAB ...,

Closed packed crystal structures

Closed packed crystal structures

This yields an ABCABCABC . . . stacking sequence;

the atomic alignment repeats every third plane.

These planes are of the (111) type

For FCC structure,

the centers of the third

plane are situated

over the C sites of the first plane.

A sites

B B

B

B B

B B

C sites C C

C A

B

• ABCABC... Stacking Sequence

• 2D Projection

FCC Unit Cell

FCC Stacking Sequence

B B

B

B B

B B B sites C C

C A

C C

C A

A

B C

● The HCP metals: Cd, Mg, Ti, and Zn.

● top and bottom faces consist of six atoms that

form regular hexagons and surround a single atom

in the center.

● Another plane that provides three additional

atoms to the unit cell is situated between the top

and bottom planes. The atoms in this mid-plane

have as nearest neighbors atoms in both of the

adjacent two planes.

Hexagonal close packed (HCP) crystal structure

● The equivalent of six atoms is contained in

each unit cell

● one-sixth of each of the 12 top and bottom

face corner atoms, one-half of each of the

2 center face atoms, and all 3 midplane

interior atoms.:

12 x 1/6 + 2 x ½ + 3 = 2 +1 + 3 = 6

corner face midplane

Hexagonal close packed (HCP) crystal structure

Closed packed crystal structures

● both FCC and HCP crystal structures have

atomic packing factors of 0.74, which is

the most efficient packing of equal-sized

spheres or atoms.

● these two crystal structures may be

described in terms of close-packed planes

of atoms (i.e., planes having a maximum

atom or sphere packing density)

• Coordination # = 12

• ABAB... Stacking Sequence

• APF = 0.74

• 3D Projection • 2D Projection

Hexagonal Close-Packed Structure (HCP)

6 atoms/unit cell

ex: Cd, Mg, Ti, Zn

• c/a = 1.633

c

a

A sites

B sites

A sites Bottom layer

Middle layer

Top layer

Unit cell volume

Sin 60 = h /a h = a sin 60

Atomic packing factor

2R=a; R=a/2

ideal c/a ratio in HCP

h2= a2+(a/2)2

x=(2/3)h

x2 + (c/2)2 = a2

a/2

see you next week!